Comptes Rendus
Numerical Analysis
A superconvergent projection method for nonlinear compact operator equations
[Une méthode de projection superconvergente pour les équations d'opérateurs nonlinéaires compacts]
Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 215-218.

Nous proposons une méthode, basée sur une projection, pour approcher les points fixes localement uniques d'un opérateur compact. Cette méthode présente un avantage par rapport aux méthodes de Galerkin et de Galerkin itérée étudiées par K.E. Atkinson and F.A. Potra : on n'a pas besoin de conditions supplémentaires pour obtenir la superconvergence de la solution approchée vers la solution exacte.

We propose a method based on projections for approximating fixed points of a compact nonlinear operator. Under the same assumptions as in the Galerkin method, the proposed solution is shown to converge faster than the Galerkin solution.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2005.11.011

Laurence Grammont 1 ; Rekha Kulkarni 2

1 Laboratoire de mathématiques de l'université de Saint-Étienne, 23, rue du Dr. Paul Michelon, 42023 Saint Étienne cedex 2, France
2 Department of Mathematics, Indian Institute of Technology, Powai, Mumbai 400076, India
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Laurence Grammont; Rekha Kulkarni. A superconvergent projection method for nonlinear compact operator equations. Comptes Rendus. Mathématique, Volume 342 (2006) no. 3, pp. 215-218. doi : 10.1016/j.crma.2005.11.011. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2005.11.011/

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